Method for setting control parameters for model prediction control

ABSTRACT

A setting method according to the present invention determines a desired time response in an optimum servo control structure corresponding to a servo control structure of a control target, calculates a predetermined gain corresponding to the desired time response, and calculates a first weighting coefficient Qf, a second weighting coefficient Q, and a third weighting coefficient R of a predetermined Riccati equation according to the Riccati equation on the basis of the predetermined gain. The first weighting coefficient Qf, the second weighting coefficient Q, and the third weighting coefficient R are set as a weighting coefficient corresponding to a terminal cost, a weighting coefficient corresponding to a state quantity cost, and a weighting coefficient corresponding to a control input cost, respectively, in a predetermined evaluation function for model prediction control.

TECHNICAL FIELD

The present invention relates to a method for setting control parametersfor model prediction control.

BACKGROUND ART

Generally, feedback control is used in order to control a control targetto track a command trajectory. For example, a control device of anarticulated robot controls servo motors of respective joint shafts usingfeedback control so that the position of a hand of the robot tracks acommand trajectory set (taught) in advance. However, general feedbackcontrol has a problem that since a response delay occurs inevitably ineach servo motor, the actual trajectory of the robot deviates from thecommand trajectory. Techniques related to model prediction control areused to suppress such a deviation from the command trajectory.

However, even when model prediction control is used, a steady-stateoffset may occur if a target trajectory for a command changes frequentlyas in tracking control. Therefore, when a servo system is constructedusing model prediction control, the steady-state offset may beeliminated by connecting an integrator to a compensator thereof inseries. Moreover, the steady-state offset can be removed in principle byincorporating an assumed disturbance into the model by regarding thedisturbance as a new state. For example, NPL 1 and NPL 2 propose methodsfor constructing a disturbance observer and cancelling a steady-stateoffset using a disturbance estimated by the disturbance observer.

CITATION LIST Non Patent Literature

-   NPL 1: Yuta Sakurai and Toshiyuki Ohtsuka: Offset Compensation of    Continuous Time Model Predictive Control By Disturbance Estimation;    Journal of Institute of Systems, Control and Information Engineers,    Vol. 25, No. 7, pp. 10-18 (2012)-   NPL 2: U. Maeder and M. Morari: Linear offset-free model predictive    control; Automatica, Vol. 45, No. 10, pp. 2214-2222 (2009)-   NPL3: Fatima TAHIR and Toshiyuki OHTSUKA: Tuning of Performance    Index in Nonlinear Model Predictive Control by the Inverse Linear    Quadratic Regulator Design Method, SICE Journal of Control,    Measurement, and System Integration, Vol. 6, No. 6, pp. 387-395,    (2013)

SUMMARY OF INVENTION Technical Problem

When model prediction control is performed for servo control in which anoutput of a control target is controlled to track a target command, anoptimal control input is calculated according to a predeterminedevaluation function. Generally, in the predetermined evaluationfunction, a terminal cost related to a state variable of the controltarget and a stage cost related to the state variable and the controlinput are calculated, and the control input is optimized so that the sumthereof is immunized. In this case, the weighting coefficients of theterminal cost and the stage cost are set in the evaluation functionwhereby the control input is optimized in a state in which a correlationof the costs is applied.

Here, the weighting coefficients of the model prediction control cannoteasily find an immediate relationship with a time response of thecontrol target of the model prediction control. Therefore, a userrequires numerous trial-and-errors in determining the weightingcoefficients for model prediction control. Although NPL 3 discloses amethod for determining weighting coefficients for model predictioncontrol by taking a time response of a control target into considerationwhen a regulator performs model prediction control, this method cannotdeal with servo control.

The present invention has been made in view of the above-describedproblems, and an object thereof is to provide a technique for allowing auser to set weighting coefficients for model prediction controlimmediately on the basis of a time response of a control target whenmodel prediction control is performed for servo control in which anoutput of a control target is controlled to track a target command.

Solution to Problem

In the present invention, in order to solve the problems, it is assumedthat a system that linearizes a prediction model used in modelprediction control near a terminal end and an optimum servo controlstructure corresponding to a control structure that performs servocontrol using the model prediction control output the same output withrespect to the same control input. In this way, when model predictioncontrol is performed for servo control using so-called an ILQ designmethod, a user can set weighting coefficients immediately on the basisof a time response of a control target.

Specifically, the present invention provides a method for settingcontrol parameters for model prediction control (hereinafter, alsoreferred to simply as a “control parameter setting method”) related to apredetermined control target, the method being executed by a controldevice having a first integrator to which an offset between apredetermined target command and an output of the predetermined controltarget corresponding to an actual target device which is an actualtarget of servo control is input, in order to allow an output of theactual target device tracks the predetermined target command. Thecontrol device includes a model prediction control unit which has aprediction model that defines a correlation between a predeterminedexpanded state variable related to an expanded control target includingat least the predetermined control target and a control input to theexpanded control target in a form of a predetermined state equation andwhich performs the model prediction control based on the predictionmodel according to a predetermined evaluation function in a predictionsection having a predetermined time width with respect to thepredetermined target command and outputs a value of the control input atleast at an initial time point of the prediction section. Moreover, apredetermined state variable which is a portion of the predeterminedexpanded state variable and is related to the predetermined controltarget includes a predetermined integral term represented by a productof the offset and a predetermined integral gain.

The setting method includes: a time response determining step ofdetermining a desired time response in an optimum servo controlstructure which includes a virtual integrator virtually corresponding tothe first integrator and is related to a virtual control targetvirtually corresponding to the expanded control target and in which,when a virtual target command for the virtual control target is r1, avirtual control input to the virtual control target is a virtual controlinput u1, and a virtual output of the virtual control target is y1, thevirtual control input u1 is represented by Equation 1 below including astate feedback gain K_(F) and an integral gain K_(I); a gain calculationstep of calculating the state feedback gain K_(F) and the integral gainK_(I) corresponding to the desired time response; a weightingcoefficient calculation step of calculating a second weightingcoefficient Q and a third weighting coefficient R among a firstweighting coefficient Qf, the second weighting coefficient Q, and thethird weighting coefficient R in a predetermined Riccati equationrepresented by Equation 3 below on the basis of the state feedback gainK_(F) and the integral gain K_(I) when the control input to the expandedcontrol target is u, the output of the expanded control target is y, theoffset is e, the predetermined state variable is x, and a state equationrelated to the predetermined control target is represented by Equation 2below; and a setting step of setting the second weighting coefficient Qas a weighting coefficient corresponding to a state quantity cost whichis a stage cost related to the predetermined state variable and settingthe third weighting coefficient R as a weighting coefficientcorresponding to a control input cost which is a stage cost related tothe control input in the predetermined evaluation function.

Furthermore, in the weighting coefficient calculation step, the firstweighting coefficient Qf may be further calculated. In this case, in thesetting step, the first weighting coefficient Qf may be set as theweighting coefficient corresponding to the terminal cost related to thepredetermined state variable.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 1} \rbrack & \; \\{{u\; 1} = {{{- K_{F}}x} + {K_{I}{\int{( {{r1} - {y1}} ){dt}}}}}} & ( {{Equation}\mspace{14mu} 1} ) \\\{ {\begin{matrix}{\overset{.}{x} = {{Ax} + {Bu}}} \\{\overset{.}{z} = {{- {Cx}} + r}}\end{matrix},{\begin{bmatrix}\overset{.}{x} \\\overset{.}{z}\end{bmatrix} = {{{\begin{bmatrix}A & 0 \\{- C} & 0\end{bmatrix}\begin{bmatrix}x \\z\end{bmatrix}} + {\begin{bmatrix}B \\O\end{bmatrix}u} + {\begin{bmatrix}0 \\r\end{bmatrix}e}} = {{r - y} = \overset{.}{z}}}}}  & ( {{Equation}\mspace{14mu} 2} ) \\{{{{Q_{f}A_{e}} + {A_{e}^{T}Q_{f}} - {Q_{f}B_{e}R^{- 1}B_{e}^{T}Q_{f}} + Q} = 0}{{{{where}\mspace{14mu} A_{e}} = \begin{bmatrix}A & 0 \\C & 0\end{bmatrix}},{B_{e} = \begin{bmatrix}B \\0\end{bmatrix}}}} & ( {{Equation}\mspace{14mu} 3} )\end{matrix}$

In the control parameter setting method of the present disclosure,weighting coefficients for model prediction control used for allowing afinal output of an actual target device to track a predetermined targetcommand are calculated by determining a time response of an output of avirtual control target (that is, a time response of an output of anexpanded control target) in the optimum servo control structureaccording to Equation 1. That is, by using the control parameter settingmethod, a user can easily acquire weighting coefficients for modelprediction control corresponding to the time response recognizableimmediately and does not need to repeat trial-and-errors related toweighting coefficients for model prediction control for tracking atarget command unlike the conventional technique. The predeterminedcontrol target may be an actual target device and may be an actualtarget model that models the actual target device. When thepredetermined control target is an actual target model, the expandedcontrol target is an expansion system model including the actual targetmodel.

In the control parameter setting method, the expanded control target mayinclude the predetermined control target only, and a portion of thepredetermined expanded state variable may be identical to thepredetermined state variable. The control parameter setting methodaccording to the present disclosure can be applied to a form in whichthe expanded control target is identical to the predetermined controltarget, and therefore, a user does not need to repeat trial-and-errorsrelated to weighting coefficients for model prediction control.

As another method, in the control parameter setting method, the controlinput may be a jerk input to the predetermined control target, and theexpanded control target may include additional integrator that performsa predetermined integration process with respect to the jerk input inaddition to the predetermined control target. In this case, theprediction model may define a correlation between the jerk input and thepredetermined expanded state variable including the predetermined statevariable related to the predetermined control target and a statevariable related to the additional integrator. The control parametersetting method according to the present disclosure can be applied to aform in which the expanded control target includes additional integratorfor the jerk input together with the predetermined control target, andtherefore, a user does not need to repeat trial-and-errors related toweighting coefficients for model prediction control.

Furthermore, a filter unit that performs an attenuation process at apredetermined frequency with respect to a control input based on thepredetermined target command may be included in the predeterminedcontrol target and the expanded control target including the additionalintegrator whereby a further expanded control target is formed in thecontrol device, and the control parameter setting method according tothe present disclosure may be the control parameter setting method forthe model prediction control executed by the control device. In thiscase, a state variable related to the further expanded control targetmay include a state variable related to the filter unit in addition tothe predetermined expanded state variable, and the prediction model maydefine a correlation between the jerk input and the predeterminedexpanded state variable and the state variable related to the filterunit. In the weighting coefficient calculation step, the secondweighting coefficient Q and the third weighting coefficient R may becalculated on the basis of the state feedback gain K_(F) and theintegral gain K_(I), and zeros may be added to the second weightingcoefficient as a weighting coefficient corresponding to the statevariable related to the filter unit so as to correspond to the furtherexpanded control target to obtain a new second weighting coefficient. Inthe setting step, the new second weighting coefficient may set as theweighting coefficient corresponding to the state quantity cost and thethird weighting coefficient R may be set as the weighting coefficientcorresponding to the control input cost in the predetermined evaluationfunction.

Furthermore, in the weighting coefficient calculation step, the firstweighting coefficient Qf, the second weighting coefficient Q, and thethird weighting coefficient R corresponding to the expanded controltarget may be calculated on the basis of the state feedback gain K_(F)and the integral gain K_(I). In this case, in the setting step, thefirst weighting coefficient Qf may be further set as the weightingcoefficient corresponding to the terminal cost in the predeterminedevaluation function.

In these cases, the further expanded control target includes a filterunit in addition to the predetermined control target and the additionalintegrator, and a state variable related to the filter unit is appliedto the prediction model for the model prediction control. In this way,with the model prediction control, it is possible to realize idealtracking of the target command while suppressing vibration of the outputof the predetermined control target. Here, the attenuation processitself by the filter unit is not to be substantially applied tooptimization of the control input according to the predeterminedevaluation function. Therefore, in the weighting coefficient calculationstep, zeros may be added to the second weighting coefficient calculatedfor the expanded control target including the predetermined controltarget and the additional integrator as a weighting coefficientcorresponding to the state variable related to the filter unit to obtaina new second weighting coefficient, which can be employed as a finalweighting coefficient for the model prediction control. In this way, itis possible to eliminate user's trial-and-errors related to weightingcoefficients for model prediction control.

The filter unit may be configured as a notch filter in which thepredetermined frequency is used as a central frequency of theattenuation process or a low-pass filter in which the predeterminedfrequency is used as a cutoff frequency of the attenuation process.Moreover, the filter unit may be configured as a filter other than thesefilters.

Advantageous Effects of Invention

A user can set weighting coefficients for model prediction controlimmediately on the basis of a time response of a control target whenmodel prediction control is performed for servo control in which anoutput of a control target is controlled to track a target command.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a diagram illustrating an example of a control structure towhich a method for setting control parameters for model predictioncontrol is applied.

FIG. 1B is a diagram illustrating an optimal servo structurecorresponding to the control structure illustrated in FIG. 1A.

FIG. 1C is an integration-type ILQ servo control structure obtained byreconstructing the optimal servo structure illustrated in FIG. 1B.

FIG. 2 is a diagram illustrating a control structure of a servo driveraccording to a first configuration example.

FIG. 3 is a diagram illustrating a control structure of a servo driveraccording to the first configuration example.

FIG. 4 is a diagram illustrating the flow of a method for settingweighting coefficients (control parameters) of an evaluation functionfor model prediction control executed in the servo driver according tothe first configuration example.

FIG. 5 is a diagram illustrating the result of trackability when anactual plant having two control axes is servo-controlled by the servodriver according to the first configuration example.

FIG. 6 is a diagram illustrating a control structure of a servo driveraccording to a second configuration example.

FIG. 7 is a diagram illustrating the result of trackability when anactual plant having two control axes is servo-controlled by the servodriver according to the second configuration example.

FIG. 8 is a diagram illustrating a control structure of a servo driveraccording to a third configuration example.

FIG. 9 is a diagram illustrating a transfer function related to afurther expanded plant in the servo driver according to the thirdconfiguration example.

FIG. 10 is a diagram illustrating a detailed control structure relatedto a further expanded plant.

FIG. 11 is a diagram illustrating an example of weighting coefficientscorresponding to a state quantity cost in the third configurationexample.

FIG. 12 is a diagram illustrating the result of trackability when anactual plant having two control axes is servo-controlled by the servodriver according to the third configuration example.

FIG. 13 is a diagram illustrating a control structure of a standard PLCaccording to a fourth configuration example.

FIG. 14 is a diagram illustrating a control structure of a standard PLCaccording to a fifth configuration example.

FIGS. 15A and 15B are diagrams illustrating an overall configuration ofa robot arm which is a plant according to the fifth configurationexample.

DESCRIPTION OF EMBODIMENTS Application Example

An example of a scene in which a method for setting control parametersfor model prediction control according to the present invention isapplied will be described with reference to FIGS. 1A to 1C. FIG. 1Aillustrates a control structure that executes tracking control (servocontrol) for causing an output y of a plant 103 which is a controltarget to track a target command r. In the control structure, modelprediction control is executed by the model prediction control unit 102,whereby tracking control to the target command r is realized, a controlinput to the plant 103 calculated by the model prediction control isreferred to as u, and a state variable related to the plant 103 used forcalculation of the model prediction control is referred to as x.

In the control structure, an offset e (e=r−y) between the target commandr and the output y of the plant 103 is input to a first integrator 101.An output z of the first integrator 101 is also included in the statevariable x used for calculation of the model prediction control.Therefore, the model prediction control unit 102 performs modelprediction control using the state variable x related to the plant 103and the output z of the first integrator 101. Moreover, the statevariable x related to the plant 103 is passed through a block 104whereby the output y of the plant 103 is generated. Therefore, the stateequation related to the actual plant 6 is represented by Equation 4below.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 2} \rbrack & \; \\\{ {\begin{matrix}{\overset{.}{x} = {{Ax} + {Bu}}} \\{\overset{.}{z} = {{- {Cx}} + r}}\end{matrix},{\begin{bmatrix}\overset{.}{x} \\\overset{.}{z}\end{bmatrix} = {{{\begin{bmatrix}A & 0 \\{- C} & 0\end{bmatrix}\begin{bmatrix}x \\z\end{bmatrix}} + {\begin{bmatrix}B \\0\end{bmatrix}u} + {\begin{bmatrix}0 \\r\end{bmatrix}{where}\mspace{14mu} e}} = {{r - y} = \overset{.}{z}}}}}  & ( {{Equation}\mspace{14mu} 4} )\end{matrix}$

Here, model prediction control executed by the model prediction controlunit 102 will be described. The model prediction control unit 102executes model prediction control (Receding Horizon control) using thestate variable x including the output z of the first integrator 101 andthe control input u to the plant 103 output by the model predictioncontrol unit 102. The model prediction control unit 102 has a predictionmodel that defines a correlation between the state variable x and thecontrol input u by the following state equation (Equation 5). Equation 5below is a nonlinear state equation. Predetermined physicalcharacteristics of the plant 103, for example, may be applied to theprediction model.

[Math. 3]

{dot over (x)}(t)=P(x(t)u(t))   (Equation 5)

Here, the model prediction control unit 102 performs model predictioncontrol based on the prediction model represented by Equation 5according to the evaluation function illustrated in Equation 6 below ina prediction section having a predetermined time width T using the statevariable x and the control input u as an input.

[Math. 4]

J=φ(x(t+T))+∫_(t) ^(t+T) L(x(τ),u(τ))dτ   (Equation 6)

The first term on the right side of Equation 6 is a terminal cost, andthe second terminal on the right side is a stage cost. The terminal costcan be represented by Equation 7 below, and the stage cost can berepresented by Equation 8 below.

[Math. 5]

φ(x(t+T))=(xref−x)^(T)(k)Qf(xref−x)(k)   (Equation 7)

[Math. 6]

L=½((xref−x)^(T)(k)Q(xref−x)(k)+(uref−u)^(T)(k)R(uref−u)(k))   (Equation8)

Here, xref (k) represents a target state quantity at time point k, x(k)represents a calculated state quantity at time point k, uref(k)represents a target control input in a normal state at time point k, andu(k) represents a calculated control input at time point k. Qf inEquation 7 is a coefficient (a weighting coefficient) indicating aweighting factor of a state quantity of the terminal cost. Moreover, Qand R in Equation 8 are a coefficient (a weighting coefficient)representing a weighting factor of a state quantity of the stage costand a coefficient (a weighting coefficient) representing a weightingfactor of a control input, respectively. Therefore, the first term onthe right side of Equation 8 means a stage cost related to a statequantity and is referred to as a “state quantity cost”, and the secondterm on the right side means a stage cost related to a control input andis referred to as a “control input cost”.

A value of the control input u at initial time point t of the predictionsection, calculated in the model prediction control on the basis of theabove is output as a control input u to the plant 103 corresponding tothe target command r at that time point t. In the model predictioncontrol, a prediction section having a predetermined time width T is setat each control time point and the control input u at the control timepoint is calculated according to the evaluation function of Equation 6and is supplied to the plant 103. A problem of calculating an operationamount that optimizes a value of an evaluation function J having such aform as in Equation 6 is a problem widely known as an optimal controlproblem, and an algorithm for calculating a numerical solution thereofis disclosed as a known technique. A continuous deformation method canbe exemplified as such a technique, and the details thereof aredisclosed, for example, in “A continuation/GMRES method for fastcomputation of nonlinear receding horizon control”, T. Ohtsuka,Automatica, Vol. 40, pp. 563-574 (2004), for example.

In a continuous deformation method, an input U(t) to model predictioncontrol is calculated by solving a simultaneous linear equation relatedto the input U(t) illustrated in Equation 9 below. Specifically,Equation 9 below is solved and dU/dt is numerically integrated to updatethe input U(t). In this manner, since the continuous deformation methoddoes not perform repeated computation, it is possible to suppress acomputational load for calculating the input U(t) at each time point asmuch as possible.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 7} \rbrack & \; \\{{\frac{\partial F}{\partial U}\overset{.}{U}} = {{{- \zeta}\; F} - {\frac{\partial F}{\partial x}\overset{.}{x}} - \frac{\partial F}{\partial t}}} & ( {{Equation}\mspace{14mu} 9} )\end{matrix}$

Where F and U(t) are represented by Equation 10 below.

$\begin{matrix}{\mspace{79mu} \lbrack {{Math}.\mspace{11mu} 8} \rbrack} & \; \\{{{F( {{U(t)},{x(t)},t} )} = \begin{bmatrix}{\frac{\partial H}{\partial u}( {{x_{0}^{*}(t)},{u_{0}^{*}(t)},{\lambda_{1}^{*}(t)},{\mu_{0}^{*}(t)}} )} \\{C( {{x_{0}^{*}(t)},{u_{0}^{*}(t)}} )} \\\ldots \\{\frac{\partial H}{\partial u}( {{x_{{N\_}1}^{*}(t)},{u_{{N\_}1}^{*}(t)},{\lambda_{N}^{*}(t)},{\mu_{{N\_}1}^{*}(t)}} )} \\{C( {{x_{{N\_}1}^{*}(t)},{u_{{N\_}1}^{*}(t)}} )}\end{bmatrix}}\mspace{20mu} {{U(t)} = \lbrack {{u_{0}^{*T}(t)},{\mu_{0}^{*T}(t)},\ldots \;,{u_{{N\_}1}^{*T}(t)},{\mu_{{N\_}1}^{*T}(t)}} \rbrack}} & ( {{Equation}\mspace{14mu} 10} )\end{matrix}$

Where H is a Hamiltonian, λ is a costate, and μ is a Lagrange multiplierof constraints C=0.

Next, a method for setting the terminal cost of the evaluation functionand the weighting coefficient related to the stage cost will bedescribed. The setting method includes a time response determining step,a gain calculation step, a weighting coefficient calculation step, and asetting step.

(Time Response Determining Step)

Here, an optimal servo structure related to a virtual plant virtuallycorresponding to the plant 103 is illustrated in FIG. 1B. The optimalservo structure includes a virtual integrator 201 virtuallycorresponding to the first integrator 101, a virtual plant 203 virtuallycorresponding to the plant 103, and a virtual block 204 virtuallycorresponding to the block 104. When a virtual target command is r1, avirtual control input to the virtual plant 203 is a virtual controlinput u1, and an output of the virtual plant 203 is y1, a virtualcontrol input u1 is represented by Equation 11 below. Here, K_(F) is astate feedback gain and K_(I) is an integral gain.

[Math. 9]

u1=−K _(F) x+K _(I)∫(r1−y1)dt   (Equation 11)

The optimal servo structure formed in this manner corresponds to astructure in which a prediction model of the control structureillustrated in FIG. 1A is linearized near a terminal end. As a result,in the control structure of FIG. 1A and the optimal servo structure ofFIG. 1B, when the variables x, z, and u which are evaluation items andthe weighting coefficients Qf, Q, and R are focused on, the input/outputof the optimal servo structure can be correlated with the input/outputof the control structure illustrated in FIG. 1A (that is, theinput/output of the control structure in which model prediction controlis performed by the model prediction control unit 102). Based on thisfact, first, in the time response determining step, a desired timeresponse of the optimal servo structure is determined. That is, thisdetermination substantially means determining a time response that isexpected to be realized in the control structure illustrated in FIG. 1A.

(Gain Calculation Step)

Subsequently, in the gain calculation step, a state feedback gain K_(F)and an integral gain K_(I) of the optimal servo structure correspondingto the desired time response determined in the statistic process arecalculated. Calculates of these gains are realized using a method(hereinafter referred to as a “reconstruction method”) of reconstructingan optimum servo control structure illustrated in FIG. 1B anintegration-type ILQ servo control structure illustrated in FIG. 1C.Components common with the optimal servo structure of FIG. 1B and theintegration-type ILQ servo control structure of FIG. 1C will be denotedby the same reference numerals, and the description thereof will beomitted. A difference of the integration-type ILQ servo controlstructure of FIG. 1C from the optimum servo control structure of FIG. 1Bis that a gain adjustment parameter block 206 common to the statefeedback gain K_(F) and the integral gain K_(I) are tied up, and as aresult, in the integration-type ILQ servo control structure, the gainsare represented by a first reference optimal gain K_(F) ⁰ (indicated by205′) and a second reference optimal gain K_(I) ⁰ (indicated by 202′)which are reference optimal gains. Moreover, the adjustment parameter ofthe block 206 is represented by Equation 12 below, and Σ in the equationis a responsiveness matrix designating a time responsiveness in afirst-order lag form, and V is a non-interference matrix for simplifyingcomputation. When the integration-type ILQ servo control structure isreconstructed by such a reconstruction method, the state feedback gainK_(F) and the integral gain K_(I) for realizing a time response ideallyapproximated in the first-order lag form to the time response determinedthrough the determination of the adjustment parameter and thecalculation of the first reference optimal gain K_(F) ⁰ and the secondreference optimal gain K_(I) ⁰ are calculated.

[Math. 10]

Adjustment parameter V ⁻¹ ΣV   (Equation 12)

(Weighting Coefficient Calculation Step)

Subsequently, in the weighting coefficient calculation step, based onthe fact that the state equation related to the plant 103 is representedby Equation 4 described above, a first weighting coefficient Qf, asecond weighting coefficient Q, and a third weighting coefficient R of apredetermined Riccati equation is calculated according to the Riccatiequation represented by Equation 13 below on the basis of the statefeedback gain K_(F) and the integral gain K_(I) calculated in the gaincalculation step.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 11} \rbrack & \; \\{{{{Q_{f}A_{e}} + {A_{e}^{T}Q_{f}} - {Q_{f}B_{e}R^{- 1}B_{e}^{T}Q_{f}} + Q} = 0}{{{{where}\mspace{14mu} A_{e}} = \begin{bmatrix}A & 0 \\C & 0\end{bmatrix}},{B_{e} = \begin{bmatrix}B \\0\end{bmatrix}}}} & ( {{Equation}\mspace{14mu} 13} )\end{matrix}$

(Setting Step)

The present applicant has found that the first weighting coefficient Qf,the second weighting coefficient Q, and the third weighting coefficientR calculated in the weighting coefficient calculation step can beideally used as the weighting coefficients of the evaluation functionrepresented by Equations 7 and 8. Therefore, in the setting step, thefirst weighting coefficient Qf is set as the weighting coefficientcorresponding to the terminal cost of the evaluation function, thesecond weighting coefficient Q is set as the weighting coefficientcorresponding to the state quantity cost, and the third weightingcoefficient R is set as the weighting coefficient corresponding to thecontrol input cost.

According to such a control parameter setting method, a user canimmediately set the weighting coefficients Qf, Q, and R of theevaluation function with respect to the time response of the plant 103expected by the model prediction control, and therefore, can alleviatethe load related to a parameter setting operation of the user. When themodel prediction control unit 102 performs model prediction controlthrough such parameter setting, an integration amount serving as adriving source of servo control is adjusted ideally in the servo controlfor tracking using the model prediction control, and it is possible torealize servo control suppressing an overshoot without using adisturbance observer which requires difficult adjustment such asexpansion of a disturbance model or design of an observer gain as in theconventional technique.

First Configuration Example

FIG. 2 is a diagram illustrating an overall configuration of a controlsystem according to a first configuration example. The control systemincludes a network 1, a servo driver 4, and a standard PLC (ProgrammableLogic Controller) 5. The servo driver 4 is a control device thatexecutes model prediction control for servo-controlling an actual plant(hereinafter simply referred to as an “actual plant”) 6 including amotor 2 and a load device 3. In the control system, the servo driver 4performs servo control involving model prediction control with respectto the actual plant 6 so that the output of the actual plant 6 tracks atarget command transmitted from the standard PLC 5. With this modelprediction control, the servo driver 4 generates a control input forperforming servo control of the actual plant 6 on the basis of thetarget command received from the standard PLC 5. Generation of thecontrol input by the servo driver 4 will be described later. In thiscase, examples of the load device 3 that constitutes the plant 6 includevarious machine apparatuses (for example, an industrial robot arm and aconveying apparatus), and the motor 2 is incorporated in the load device3 as an actuator that drives the load device 3. For example, the motor 2is an AC servo motor. An encoder (not illustrated) is attached to themotor 2, and a parameter signal (a position signal, a velocity signal,and the like) related to an operation of the motor 2 is transmitted tothe servo driver 4 as a feedback signal by the encoder.

The standard PLC 5 generates a target command related to an operation(motion) of the plant 6 and transmits the same to the servo driver 4.The servo driver 4 receives the target command from the standard PLC 5via the network 1 and receives the feedback signal output from theencoder connected to the motor 2. The servo driver 4 supplies a drivingcurrent to the motor 2 so that the output of the plant 6 tracks thetarget command. The supplied current is an AC power delivered from an ACpower supply to the servo driver 4. In the present embodiment, the servodriver 4 is a type that receives a three-phase AC power but may be atype that receives a single-phase AC power.

Here, the servo driver 4 has a control structure illustrated in FIG. 3in order to realize the servo control of the actual plant 6. The targetcommand supplied from the standard PLC 5 to the servo driver 4 isreferred to as r. The servo driver 4 includes a first integrator 41, astate acquisition unit 42, and a model prediction control unit 43. Theprocesses performed by the first integrator 41, the state acquisitionunit 42, and the model prediction control unit 43 are computed andexecuted by an arithmetic processing device mounted in the servo driver4. In the control structure of the servo driver 4, an offset e (e−r−y)between the target command r transmitted from the standard PLC 5 and theoutput y of the actual plant 6 fed back by a feedback system is input tothe first integrator 41. The output z of the first integrator 41 isinput to the model prediction control unit 43 through the stateacquisition unit 42.

Here, the state acquisition unit 42 acquires a state variable xincluding the state related to the actual plant 6 and the output z ofthe first integrator 41, provided to the model prediction controlperformed by the model prediction control unit 43. For example, thestate acquisition unit 42 can acquire predetermined informationgenerated from an output signal of the encoder connected to the motor 2included in the actual plant 6 as the state variable included in thestate x. Moreover, a predetermined parameter (for example, the positionof an output unit of the load device 3) related to the load device 3included in the actual plant 6 may be acquired as the state variable x.Furthermore, in the present embodiment, the state acquisition unit 42also acquires the output z of the first integrator 41 as the statevariable included in the state x. The model prediction control unit 43executes model prediction control (Receding Horizon control) using thestate variable x acquired by the state acquisition unit 42 and a controlinput u to the actual plant 6 input by the model prediction control unit43.

In the present specification, a virtual control configuration to whichthe control input u is input and which includes at least the actualplant 6 is formed as an expanded plant 60. The expression “expanded” asused herein means that the actual plant 6 solely or a combination withthe actual plant 6 is regarded as a virtual control target. The expandedplant 60 is also referred to as an “expanded plant 60”. In the controlstructure illustrated in FIG. 3, a control configuration other than theactual plant 6 is not included in the expanded plant 60 and the expandedplant 60 and the actual plant 6 are identical. However, FIG. 6 to bedescribed later, for example, illustrates an example in which the actualplant 6 and a second integrator 6 a are included in the expanded plant60. The output of the expanded plant 60 is identical to the output ofthe actual plant 6.

Here, returning to FIG. 3, an offset e between the command r and theoutput y of the expanded plant 60 is input to the first integrator 41,and the output z of the first integrator 41 is input to the modelprediction control unit 43 through the state acquisition unit 42 wherebythe model prediction control is performed. Based on the controlstructure including the first integrator 41, the prediction modelincluded in the model prediction control unit 43 is formed asillustrated in Equation 14 below, for example. Predetermined physicalcharacteristics of the actual plant 6 are applied to Equation 14.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 12} \rbrack & \; \\\begin{matrix}{{\overset{.}{x}(t)} = {P( {{x(t)},{u(t)}} )}} \\{= \begin{bmatrix}{\overset{.}{x}}_{1} \\{\overset{¨}{x}}_{1} \\{\overset{.}{z}}_{1}\end{bmatrix}} \\{= \begin{bmatrix}{\overset{.}{x}}_{1} \\\frac{u_{1}}{M_{1}} \\{( {x_{f\; 1} - x_{1}} ) \cdot K_{i\; 1}}\end{bmatrix}}\end{matrix} & ( {{Equation}\mspace{14mu} 14} )\end{matrix}$

A subscript “1” in Equation 14 indicates the number of control axescontrolled by the servo driver 4, and in the present embodiment, sincethe number of control axes is 1, the subscripts of the respectivevariables of the prediction model illustrated in Equation 14 are “1”. Astate variable x₁ indicates an output position of the actual plant 6 andis a parameter fed back as the output y of the actual plant 6. Moreover,x_(f1) indicates a position command r to the control axis. Therefore,(x_(f1)−x₁) in the prediction model indicates the offset e. It can beunderstood that the prediction model includes an integral termrepresented by a product of the offset e (=x_(f1)−x₁) and apredetermined integral gain K_(i1). In this way, it is easy to adjust anintegration amount serving as a driving source of the servo controlperformed by the servo driver 4 which uses model prediction control, andit is easy to realize servo control suppressing an overshoot withoutusing a disturbance observer which requires difficult adjustment such asexpansion of a disturbance model or design of an observer gain as in theconventional technique.

Furthermore, in the servo driver 4, the predetermined integral gainK_(i1) of the integral term included in the prediction model illustratedin Equation 14 may be adjusted on the basis of the offset e.Specifically, the predetermined integral gain K_(i1) is adjusted so thatthe value of the predetermined integral gain K_(i1) increases as themagnitude of the offset e decreases. For example, the transition of thepredetermined integral gain K_(i1) may be set so that the predeterminedintegral gain K_(i1) is 0 when the magnitude of the offset e is equal toor larger than a predetermined threshold, the value of the predeterminedintegral gain K_(i1) approaches abruptly 1 as the magnitude of theoffset e approaches 0 when the magnitude of the offset e is smaller thanthe predetermined threshold, and the predetermined integral gain K_(i1)is 1 which is the largest value when the magnitude of the offset e is 0.In this manner, since the predetermined integral gain K_(i1) can beadjusted on the basis of the magnitude of the offset e, when an output y(x₁) of the expanded plant 60 (the actual plant 6) deviates far from acommand x_(f1), the value of the predetermined integral gain K_(i1) isadjusted to be small, and an integration amount for servo control isadjusted so as not to accumulate. Moreover, since the value of thepredetermined integral gain K_(i1) is adjusted to be large when theamount of deviation of the output y(x₁) of the expanded plant 60 (theactual plant 6) from the command x_(f1) decreases (that is, themagnitude of the offset e decreases), it is possible to effectivelyenhance the trackability of servo control. By varying the value of thepredetermined integral gain K_(i1) in this manner, it is possible toachieve both suppression of an overshoot and improvement in thetrackability of servo control.

In adjustment of the predetermined integral gain K_(i1), data related tocorrelation between the offset e and the predetermined integral gainK_(i1) may be stored in the memory of the servo driver 4, and in thatcase, the predetermined integral gain K_(i1) is adjusted by accessingthe data.

Here, in order to realize the model prediction control by the servodriver 4 having the control structure illustrated in FIG. 3, it isnecessary to appropriately set the control parameters related to themodel prediction control (that is, the weighting coefficients (thefirst, second, and third weighting coefficients Qf, Q, and R) of theevaluation function illustrated in Equations 6 to 8). Therefore, aparameter setting method of setting these weighting coefficients to theevaluation function will be described with reference to FIG. 4. FIG. 4is a diagram illustrating the flow of a parameter setting method, andthis method includes a time response determining step, a gaincalculation step, a weighting coefficient calculation step, and asetting step.

First, a time response determining step performed in S101 will bedescribed. In the time response determining step, as described above, adesired time response of the optimal servo structure illustrated in FIG.1B (that is, a time response that is expected to be realized in thecontrol structure illustrated in FIG. 1A) is determined. Specifically, arelative order di and a non-interference matrix D of the optimal servostructure are calculated according to Equation 15 below.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 13} \rbrack & \; \\{{D = \begin{bmatrix}{c_{1}A^{d_{1 - 1}}B} \\\ldots \\{c_{m}A^{d_{m - 1}}B}\end{bmatrix}},{d_{i}:={\min \{ {k:{{c_{i}A^{k - 1}B} \neq 0}} \} ( {1 \leq i \leq m} )}}} & ( {{Equation}\mspace{14mu} 15} )\end{matrix}$

Subsequently, a stabilization polynomial Φi(s) of order di having a rootof a pole si defined as a reciprocal of a time constant Ti based on thedesired time response of the optimal servo structure is set according toEquation 16 below.

[Math. 14]

Ø_(i)(s)==(s−s _(i))^(d) ^(i) , s _(i)=−1/T _(i)   (Equation 16)

Therefore, in the time response determining step, the above-describedprocess is performed on the basis of the time response in the optimalservo structure set by taking the time response expected to be realizedin the control structure illustrated in FIG. 1A into consideration.

Next, the gain calculation step performed in S102 will be described. Inthe gain calculation step, the state feedback gain K_(F) and theintegral gain K_(I) of the optimal servo structure are calculated. Forthis, first, a non-interference gain K is calculated on the basis ofEquation 17 below.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 15} \rbrack & \; \\{{K = {D^{- 1}N_{\varnothing}}},{N_{\varnothing}:=\begin{bmatrix}{c_{1}{\varnothing_{1}(A)}} \\\ldots \\{c_{m}{\varnothing_{m}(A)}}\end{bmatrix}}} & ( {{Equation}\mspace{14mu} 17} )\end{matrix}$

Subsequently, the first reference optimal gain K_(F) ⁰ and the secondreference optimal gain K_(I) ⁰ of the integration-type ILQ servo controlstructure (see FIG. 10) obtained by reconstructing the optimal servostructure according to the reconstruction method are calculated on thebasis of Equation 18 below.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 16} \rbrack & \; \\{\begin{matrix}{\lbrack {K_{F}^{0}\mspace{14mu} K_{I}^{0}} \rbrack = {\lbrack {K\mspace{14mu} I} \rbrack \Gamma^{- 1}}} \\{= {( {{CA}_{K}^{- 1}B} )^{- 1}\lbrack {{CA}_{K}^{- 1}\mspace{14mu} - I} \rbrack}}\end{matrix}{{{where}\mspace{14mu} \Gamma} = \begin{bmatrix}A & B \\C & 0\end{bmatrix}}{A_{K} = {A - {BK}}}} & ( {{Equation}\mspace{14mu} 18} )\end{matrix}$

Based on the fact that the state feedback gain K_(F) and the integralgain K_(I) are represented by Equation 19 below, a matrix Σ of theadjustment parameter is determined according to the followingprocedures. The matrix V of the adjustment parameter is a unit matrix Ias a non-interference matrix.

[Math. 17]

[K _(F) K _(I)]=V ⁻¹ ΣV[K _(F) ⁰ K _(I) ⁰]   (Equation 19)

(Σ Determination Procedure) (Procedure 1)

A maximum eigenvalue Amax of a symmetric matrix KB+(KB)^(T) is obtained,and the range of values of that constitute the matrix Σ is determined asEquation 20 below.

[Math. 18]

σ∈Σ_(a)≡{σ>0|σ>λ_(max)[KB+(KB)^(T)]}  (Equation 20)

-   -   where Σ=diag{σ₁, . . . , σ_(m)}

(Procedure 2)

Subsequently, one of the values σ in the range calculated in Procedure 1is selected, and a target correction matrix E represented by Equation 21below is calculated.

[Math. 19]

E=σI−KB−(KB)^(T)   (Equation 21)

(Procedure 3)

Subsequently, the eigenvalues of the matrix F represented by Equation 22below are calculated and the stability thereof is determined. The flowproceeds to the subsequent procedure 4 if the determination result showsthat the matrix F is stable, and the flow returns to Procedure 2 if thematrix F is unstable. In this case, the value of σ is set to a largerone in the above-mentioned range.

[Math. 20]

F=A _(K) GH  (Equation 22)

-   -   where G=BE^(−1/2), H=E^(−1/2)KA_(K)

(Procedure 4)

Subsequently, the eigenvalues of a Hamiltonian matrix H represented byEq 23 below are cald and it is determined whether these eigenvalues areon an imaginary axis. The value of σ is decreased when the eigenvaluesare not present on the inverse matrix operation, and the value of σ isincreased when any one eigenvalue is on the inverse matrix operation.After that, the flow returns to Procedure 2.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 21} \rbrack & \; \\{\Pi = \begin{bmatrix}F & {- {GG}^{T}} \\{H^{T}H} & {- F^{T}}\end{bmatrix}} & ( {{Equation}\mspace{14mu} 23} )\end{matrix}$

(Procedure 5)

When Procedures 1 to 4 are repeated and an update width of σ is equal toor smaller than a predetermined value, the value of σ is set as alower-limit value ° min. The respective values σi constituting thematrix Σ are selected within the range of σi>σmin to determine thematrix Σ.

Next, the weighting coefficient calculation step performed in S103 willbe described. In the weighting coefficient calculation step, theweighting coefficients of the evaluation function (see Equations 6 to 8)for model prediction control are calculated on the basis of apredetermined Riccati equation of an expanded offset system.Specifically, the weighting coefficients are calculated according toProcedures 6 to 9 below.

(Procedure 6)

Matrices V and R are determined as Equation 24 below.

[Math. 22]

V=I,R=V ⁻¹ E ⁻¹ V=E ⁻¹,Σ=diag{σ₁, . . . ,σ_(m)}   (Equation 24)

(Procedure 7)

Furthermore, matrices Kv and Bv are calculated by Equation 25 below.

$\begin{matrix}{\mspace{79mu} \lbrack {{Math}.\mspace{11mu} 23} \rbrack} & \; \\{{K_{V} = {{VK} = {K = {{D^{- 1}N_{\varnothing}} = {\begin{bmatrix}{c_{1}A^{d_{1 - 1}}B} \\\ldots \\{c_{m}A^{d_{m - 1}}B}\end{bmatrix}\begin{bmatrix}{c_{1}{\varnothing_{1}(A)}} \\\ldots \\{c_{m}{\varnothing_{m}(A)}}\end{bmatrix}}}}}},\mspace{20mu} {B_{V} = {{BV}^{- 1} = B}}} & ( {{Equation}\mspace{14mu} 25} )\end{matrix}$

Matrices Σ and Y satisfying Equation 26 below are calculated. When thematrix Σ determined in Procedure 5 satisfies Equation 26 below, thevalue is used as the value of the matrix Σ in Procedure 7 as it is. Whenthe matrix Σ does not satisfy Equation 26, the values of constitutingthe matrix Σ are increased.

[Math. 24]

E=Σ−K _(V) B _(V)−(K _(V) B _(V))^(T)>0

YF+F ^(T) Y+YGG ^(T) Y+H ^(T) H<0

where

F=A _(K) +GH,Reλ(F)<0,A _(K) =A−BK

G=B _(V) E ^(−1/2) ,H=E ^(−1/2) K _(V) A _(K)   (Equation 26)

(Procedure 8)

Candidates for a solution Qf of a Riccati equation of an expanded offsetsystem represented by Equation 27 below are calculated as Equation 28below.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 25} \rbrack & \; \\{{{{Q_{f}A_{e}} + {A_{e}^{T}Q_{f}} - {Q_{f}B_{e}R^{- 1}B_{e}^{T}Q_{f}} + Q} = 0}{{{{where}\mspace{14mu} A_{e}} = \begin{bmatrix}A & 0 \\C & 0\end{bmatrix}},{B_{e} = \begin{bmatrix}B \\0\end{bmatrix}}}} & ( {{Equation}\mspace{14mu} 27} ) \\\lbrack {{Math}.\mspace{11mu} 26} \rbrack & \; \\{{Q_{f} = {T_{e}^{- T}\overset{\_}{Q_{f}}T_{e}^{- 1}}}{where}} & ( {{Equation}\mspace{14mu} 28} ) \\{{\overset{\_}{Q_{f}} = \begin{bmatrix}Y & 0 \\0 & I\end{bmatrix}},{T_{e} = {\Gamma \begin{bmatrix}I & 0 \\{- K} & I\end{bmatrix}}}} & \;\end{matrix}$

Based on Equation 27 and the result of Equation 28, a matrix Q iscalculated as Equation 29 below.

[Math. 27]

Q=Q _(f) B _(e) R ⁻¹ B _(e) ^(T) Q _(f) −Q _(f) A _(e) −A _(e) ^(T) Q_(f)   (Equation 29)

Next, the setting step performed in S104 will be described. In thesetting step, the matrix Qf calculated according to Equation 28 is setas the weighting coefficient Qf (see Equation 7) corresponding to theterminal cost. Furthermore, the matrix Q calculated according toEquation 29 is set as the weighting coefficient Q corresponding to thestate quantity cost, and the matrix R illustrated in Equation 24 is setas the weighting coefficient R corresponding to the control input cost(see Equation 8).

According to the parameter setting method illustrated in FIG. 4, a usercan set the weighting coefficients Qf, Q, and R of the evaluationfunction for model prediction control immediately with respect to thetime response of the actual plant 6 expected by the model predictioncontrol and therefore can alleviate the load related to a parametersetting operation of the user. Since the model prediction control isperformed through such parameter setting, an integration amount servingas a driving source of servo control which uses the model predictioncontrol is adjusted ideally, and servo control which suppresses anovershoot can be realized. FIG. 5 illustrates a simulation result whenthe control structure illustrated in FIG. 1A is constructed with respectto the control axes of the actual plant 6 having a plurality of controlaxes through the parameter setting method and model prediction controlis executed on the respective control axes. In FIG. 5, in a workingcoordinate system in which an output of a first control axis is set asthe horizontal axis, an output of a second control axis is set as thevertical axis, the trajectory of a target command is represented by lineL1 and the trajectory of the output of the actual plant 6 is representedby line L2. As obvious from the disclosure of FIG. 5, the output of theactual plant 6 ideally tracks the target command.

In the parameter setting method illustrated in FIG. 4, the solution Qfof the Riccati equation is calculated, and the calculated Qf is set asthe weighting coefficient corresponding to the terminal cost. However,the solution Qf may not be calculated in the parameter setting method.In this case, a coefficient calculated by a known technique may beemployed as the weighting coefficient corresponding to the terminalcost.

Second Configuration Example

Servo control by the servo driver 4 according to a second configurationexample will be described with reference to FIG. 6. In the servo driver4 of this configuration example, the expanded plant 60 including theactual plant 6 is formed similarly to the first configuration example,model prediction control is performed by the model prediction controlunit 43, and the output z of the first integrator 41 is acquired by thestate acquisition unit 42 and is provided to the model predictioncontrol. In this configuration example, the second integrator 6 a andthe actual plant 6 are combined to form the expanded plant 60 asillustrated in the lower part (b) of FIG. 6.

In the expanded plant 60 of the present embodiment, the control input uis a jerk input (dτ/dt). When an expanded state variable related to theexpanded plant 60 is represented by Equation 30 below, the predictionmodel of the model prediction control unit 43 can be represented byEquation 31 below.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 28} \rbrack & \; \\{x = \begin{bmatrix}x_{1} \\{\overset{.}{x}}_{1} \\{\overset{¨}{x}}_{1} \\z_{1}\end{bmatrix}} & ( {{Equation}\mspace{14mu} 30} ) \\\lbrack {{Math}.\mspace{11mu} 29} \rbrack & \; \\{P = \begin{bmatrix}{\overset{.}{x}}_{1} \\{\overset{¨}{x}}_{1} \\\frac{u_{1}}{J_{1}} \\{( {x_{f\; 1} - x_{1}} )K_{i\; 1}}\end{bmatrix}} & ( {{Equation}\mspace{14mu} 31} )\end{matrix}$

In the prediction model of Equation 31, a correlation between theexpanded state variable and the jerk input u which is a control input isdefined. As a result, the model prediction control unit 43 generates thejerk input u which is a control input on a real-time basis and outputsthe jerk input u to the expanded plant 60. In this case, in acalculation process for calculating a stage cost of an evaluationfunction in model prediction control, the evaluation function (seeEquations 6 to 8) for model prediction control to which the weightingcoefficients are set by the parameter setting method illustrated in FIG.4 is used. Since the model prediction control is performed through suchparameter setting, an integration amount serving as a driving source ofservo control which uses the model prediction control is adjustedideally, and servo control which suppresses an overshoot can berealized. Furthermore, when a jerk input is used as the control input u,it is possible to easily suppress the largest value of jerk, andtherefore, it is possible to ideally suppress vibration of the actualplant 6 during servo control. FIG. 7 illustrates a simulation resultwhen the control structure illustrated in FIG. 1A is constructed withrespect to the control axes of the actual plant 6 having a plurality ofcontrol axes through the parameter setting method and model predictioncontrol is executed on the respective control axes. In FIG. 7, in aworking coordinate system in which an output of a first control axis isset as the horizontal axis, an output of a second control axis is set asthe vertical axis, the trajectory of a target command is represented byline L3 and the trajectory of the output of the actual plant 6 isrepresented by line L4. As obvious from the disclosure of FIG. 7, theoutput of the actual plant 6 ideally tracks the target command.

Third Configuration Example

Servo control by the servo driver 4 according to a third configurationexample will be described with reference to FIG. 8. In the servo driver4 of this configuration example, the expanded plant 60 including theactual plant 6 is formed similarly to the second configuration example,a filter unit 7 is incorporated into the expanded plant 60 to form afurther expanded plant 600, and model prediction control is performed bythe model prediction control unit 43. In this case, a difference betweena target command and the output of the further expanded plant 600 (thatis, the output of the actual plant 6) is supplied to a servo integrator41, and the output z of the servo integrator 41 and the expanded statevariable of the further expanded plant 600 are acquired by the stateacquisition unit 42 and are provided to the model prediction control.

Here, the filter unit 7 performs an attenuation process at apredetermined frequency with respect to the signal (in the presentembodiment, the control input u (jerk input) to the further expandedplant 600) input to the filter unit 7. The predetermined frequency ispreferably the frequency of vibration related to the actual plant 6which is a direct vibration suppression target during servo control. Forexample, the resonant frequency of the actual plant 6 can be set as thepredetermined frequency. Moreover, the attenuation process is a processof attenuating the gain of the signal (control input) related to thepredetermined frequency to a desired extent. Therefore, as an example,the filter unit 7 may be configured as a notch filter in which thepredetermined frequency is set as a central frequency of the attenuationprocess, or may be configured as a low-pass filter in which thepredetermined frequency is set as a cutoff frequency of the attenuationprocess. When the filter unit 7 is formed in this manner, the signal(the control input u) on which an attenuation process has been performedby the filter unit 7 is input to the expanded plant 60 including theactual plant 6. As a result, suppression of vibration in the actualplant 6 is expected during servo control of the actual plant 6, and theoutput of the actual plant 6 can approach a target in a desired period.

Here, on the basis of the fact that the further expanded plant 600includes the filter unit 7 and the expanded plant 60, the predictionmodel of the model prediction control unit 43 is determined. FIG. 9illustrates a transfer function of the filter unit 7 and a transferfunction of the expanded plant 60. An output when the control input u isinput to the filter unit 7 is represented by dν/dt, and the output dν/dtis set as an input to the expanded plant 60. A jerk input is set as thecontrol input u of the present embodiment.

FIG. 10 illustrates a control structure of the further expanded plant600 in which the transfer function of the filter unit 7 and the transferfunction of the expanded plant 60 are taken into consideration. Based onthe control structure, when the expanded state variable related to thefurther expanded plant 600 is represented by Equation 32 below, theprediction model of the model prediction control unit 43 can berepresented by Equation 33 below.

$\begin{matrix}\lbrack {{Math}.\mspace{11mu} 30} \rbrack & \; \\{x = \begin{bmatrix}x_{1} \\{\overset{.}{x}}_{1} \\{\overset{¨}{x}}_{1} \\z_{1} \\\gamma_{1} \\{\overset{.}{\gamma}}_{1}\end{bmatrix}} & ( {{Equation}\mspace{14mu} 32} ) \\\lbrack {{Math}.\mspace{11mu} 31} \rbrack & \; \\{P = \begin{bmatrix}{\overset{.}{x}}_{1} \\{\overset{¨}{x}}_{1} \\\frac{u_{1}}{J_{1}} \\{( {x_{f\; 1} - x_{1}} )K_{i\; 1}} \\{\overset{.}{\gamma}}_{1} \\{{{- \omega_{1}^{2}}\gamma_{1}} - {2\zeta_{1}\omega_{1}{\overset{.}{\gamma}}_{1}} + u_{1}}\end{bmatrix}} & ( {{Equation}\mspace{14mu} 33} )\end{matrix}$

In the prediction model of Equation 33, a correlation between theexpanded state variable and the jerk input u which is a control input isdefined. As a result, the model prediction control unit 43 generates thejerk input u which is a control input on a real-time basis and outputsthe jerk input u to the filter unit 7 included in the further expandedplant 600. Here, when the prediction model (a prediction modelrepresented by Equation 33) of this configuration example is comparedwith the prediction model (a prediction model represented by Equation31) of the second configuration example, it is understood that the orderof the prediction model of this configuration example is larger thanthat of the second configuration example by an amount corresponding tothe state variable related to the filter unit 7. Meanwhile, it cannot besaid that the state variable related to the filter unit 7 has acorrelation with evaluation (that is, evaluation of optimality based onan evaluation function) of optimality of model prediction control. Bytaking this into consideration, as for the state quantity cost among thestage costs of the evaluation function for model prediction control ofthis configuration example, a weighting coefficient corresponding to thestate quantity cost is generated using the weighting coefficientobtained in the second configuration example.

Specifically, in the weighting coefficient calculation step (S103) ofthe parameter setting method illustrated in FIG. 4, the weightingcoefficients Qf, Q, and R of the evaluation function are calculatedaccording to a prediction model that does not include the state variableof the filter unit 7 (that is, the prediction model of the secondconfiguration example (the prediction model represented by Equation31)). Since the weighting coefficient Q related to the state quantitycost among these weighting coefficients corresponds to the expandedplant 60 at this time point, the dimension thereof is different from thedimension of the expanded state variable of the further expanded plant600. Therefore, in order for the dimension of the weighting coefficientQ to correspond to the further expanded plant 600, zeros are added tothe weighting coefficient Q by an amount corresponding to the dimensioncorresponding to the state variable related to the filter unit 7, and anew weighting coefficient Q′ is generated so that the dimension of theweighting coefficient Q corresponds to the dimension of the expandedstate variable of the expanded plant 600.

Here, FIG. 11 illustrates an example of the weighting coefficient Q′related to the state quantity cost. The weighting coefficient Q′ in FIG.11 and the weighting coefficient Q which is the base thereof correspondto model prediction control in which the number of control axes is two.The prediction model (a prediction model represented by Equation 33) ofthis configuration example includes a larger number of state variablesthan that of the prediction model (the prediction model represented byEquation 31) of the second configuration example by the number (two) ofstate variables related to the filter unit 7. Therefore, zeros are addedto the weighting coefficient Q by an amount corresponding to the numberof dimensions corresponding to this difference to generate a newweighting coefficient Q′, which is illustrated in FIG. 11. As describedabove, since the weighting coefficient Q′ illustrated in FIG. 11corresponds to model prediction control in which the number of controlaxes is two, zeros are added by an amount corresponding to thedifference in the number of dimensions corresponding to two controlaxes.

In the setting step (S104) of the parameter setting method illustratedin FIG. 4, the first weighting coefficient Qf (the weighting coefficientQf calculated according to the prediction model of the secondconfiguration example) is set as the weighting coefficient correspondingto the terminal cost, the new second weighting coefficient Q′ is set asthe weighting coefficient corresponding to the state quantity cost, andthe third weighting coefficient R (the weighting coefficient Rcalculated according to the prediction model of the second configurationexample) is set as the weighting coefficient corresponding to thecontrol input cost.

Since the model prediction control is performed through such parametersetting, an integration amount serving as a driving source of servocontrol which uses the model prediction control is adjusted ideally, andservo control which suppresses an overshoot can be realized.Furthermore, since the jerk input is set as the control input u and anattenuation process is performed by the filter unit 7, it is possible toideally suppress vibration of the actual plant 6 during servo control.FIG. 12 illustrates a simulation result when the control structureillustrated in FIG. 1A is constructed with respect to the control axesof the actual plant 6 having a plurality of control axes through theparameter setting method and model prediction control is executed on therespective control axes. In FIG. 12, in a working coordinate system inwhich an output of a first control axis is set as the horizontal axis,an output of a second control axis is set as the vertical axis, thetrajectory of a target command is represented by line L5 and thetrajectory of the output of the actual plant 6 is represented by lineL6. As obvious from the disclosure of FIG. 12, the output of the actualplant 6 ideally tracks the target command.

Fourth Configuration Example

In a fourth configuration example, a control structure which is formedin the standard PLC 5 and includes a model prediction control unit 53corresponding to the model prediction control unit 43 will be describedwith reference to FIG. 13. The standard PLC 5 includes a commandgeneration unit 50, an integrator 51, a state acquisition unit 52, amodel prediction control unit 53, and an expanded plant model 560. Sincethe integrator 51, the state acquisition unit 52, and the modelprediction control unit 53 substantially correspond to the integrator41, the state acquisition unit 42, and the model prediction control unit43 illustrated in FIGS. 3, 6, and 8, respectively, the detaileddescription thereof will be omitted.

The command generation unit 50 generates a target command r forinstructing the output of the actual plant 6. In this configurationexample, the target command r is provided to model prediction control ofthe model prediction control unit 53 rather than being supplied from thestandard PLC 5 directly to the servo driver 4. Moreover, the expandedplant model 560 has an expansion system model including a plant modelthat models the expanded plant 60 illustrated in FIGS. 3 and 6 or thefurther expanded plant 600 illustrated in FIG. 8 and simulates theoutput of the expanded plant 60 or the like using the expansion systemmodel. The simulation result is used as an output y of the expandedplant model 560. The output y of the expanded plant model 560 is fedback to an input side of the integrator 51 by a feedback system.

Here, in this configuration example, an offset e (e=r−y) between thetarget command r generated by the command generation unit 50 and thefeedback output y of the expanded plant model 560 is input to theintegrator 51. An output z of the integrator 51 is input to the modelprediction control unit 53 through the state acquisition unit 52.

Here, the state acquisition unit 52 acquires the value of a statevariable included in the state x related to the expansion system model,provided to the model prediction control performed by the modelprediction control unit 53. The acquisition of the state variable by thestate acquisition unit 52 is substantially the same as acquisition ofthe state variable by the state acquisition unit 42 illustrated in thefirst to third configuration examples described above. The modelprediction control unit 53 executes model prediction control using thestate x acquired by the state acquisition unit 52 and the input u to theexpanded plant model 560 output by the model prediction control unit 53.As for the model prediction control performed by the model predictioncontrol unit 53, an integral term represented by a product of the offsete and the predetermined integral gain is included in the predictionmodel used in the model prediction control substantially similarly tothe model prediction control performed by the model prediction controlunit 43 illustrated in the first to third configuration examplesdescribed above.

Due to the control structure formed in this manner, the standard PLC 5illustrated in FIG. 13 can supply the output y which is the simulationresult of the expanded plant model 560 to the servo driver 4 as acommand for ideally tracking the target command r while suppressing theoutput of the actual plant 6 from entering an overshoot state. That is,the standard PLC 5 can suppress occurrence of a steady-state offset inthe output of the actual plant 6 while performing model predictioncontrol even when the target trajectory changes frequently according tothe target command r although the control amount of the actual plant 6which is the actual control target is not fed back directly.

In the standard PLC 5 having the control structure configured in thismanner, the parameter setting method illustrated in FIG. 4 can beapplied to the setting of the weighting coefficients of the evaluationfunction in the model prediction control. When model prediction controlis performed in the standard PLC 5 through such parameter setting, anintegration amount serving as a driving source of servo control isadjusted ideally in the servo control for tracking using the modelprediction control, it is possible to realize servo control suppressingan overshoot.

Fifth Configuration Example

A fifth configuration example relates to a modification of the standardPLC 5 having a control structure including the model prediction controlunit 53 similarly to the fourth configuration example and will bedescribed with reference to FIGS. 14 and 15. FIG. 14 illustrates acontrol structure of the standard PLC 5 according to this configurationexample, and functional units substantially the same as those of thestandard PLC 5 of the fourth configuration example will be denoted bythe same reference numerals, and the detailed description thereof willbe omitted. In this configuration example, the plant 6 is a robot arm 6illustrated in FIG. 15A. Therefore, the expanded plant model 560 has anexpansion system model to which the structure of the robot arm 6 isapplied and performs simulation of the expanded plant model 60 using theexpansion system model.

Here, the robot arm 6 which is a plant will be described with referenceto FIG. 15A. The robot arm 6 has two motors 2 (motors 2 a and 2 b)driven according to a target command from the standard PLC 5. In therobot arm 6, one end of a first arm 3 a is attached to an output shaftof the motor 2 a so that the first arm 3 a is rotated using the motor 2a as a first joint. Furthermore, a motor 2 b is disposed at the otherend of the first arm 3 a, and one end of a second arm 3 b is attached toan output shaft of the motor 2 b so that the second arm 3 b is rotatedusing the motor 2 b as a second joint. A tip 3 c of the second arm 3 bis an output unit of the robot arm 6, and an end effector for grasping apredetermined object, for example, is attached to the tip 3 c. In therobot arm 6, a plane of rotation of the first arm 3 a is the same planeas a plane of rotation of the second arm 3 b, and an x1-axis and anx2-axis are set as orthogonal coordinates for defining the plane ofrotation. This orthogonal coordinates are working coordinates related tothe robot arm 6, and the position of the tip 3 c of the robot arm 6 canbe defined on the orthogonal coordinates. The command generation unit 50of this configuration example generates a predetermined command r thatthe tip 3 c of the robot arm 6 has to track. This command r is based onthe working coordinate system (see FIGS. 15A and 15B) related to therobot arm 6.

Next, a calculation unit 570 will be described. An output y of theexpanded plant model 560 obtained when the control input u is input isbased on the working coordinate system illustrated in FIGS. 15A and 15B.Meanwhile, the motors 2 a and 2 b that form the robot arm 6 areactuators that are rotated, and a rotation coordinate system which is anindependent coordinate system different from the working coordinatesystem is set to the respective motors for servo control performed bythe servo driver 4. Therefore, the output y is not used as a targetcommand for driving the motors 2 a and 2 b as it is. Therefore, thecalculation unit 570 performs a calculation process for converting theoutput y of the expanded plant model 560 to a target command based onthe rotation coordinate system of the motors.

The calculation process of the calculation unit 570 is performedaccording to a geometric relation of an apparatus structure of the robotarm 6. FIG. 15B illustrates the apparatus structure of the robot arm 6.In FIG. 15B, the first joint at which the motor 2 a is disposed ispositioned at the origin of the working coordinate system in order tosimplify the description. When the length of the first arm 3 a is L1,the length of the second arm 3 b is L2, and the position of the tip 3 cis (x₁, x₂), the rotation angles θ1 and θ2 of the motors 2 a and 2 b canbe represented by Equation 34 below when the geometric relation of theapparatus structure of the robot arm 6 is taken into consideration. Therotation angle θ1 of the motor 2 a is defined as the angle between thex1-axis and the first arm 3 a, and the rotation angle θ2 of the motor 2b is defined as the angle between the first arm 3 a and the second arm 3b.

$\begin{matrix}{\mspace{79mu} \lbrack {{Math}.\mspace{11mu} 32} \rbrack} & \; \\{{\theta_{2} = {a\; \tan \; 2( {\frac{\pm \sqrt{( {2L_{1}L_{2}} )^{2} - \{ {L_{0}^{2} - ( {L_{1}^{2} + L_{2}^{2}} )} \}^{2}}}{2L_{1}L_{2}},\frac{L_{0}^{2} - ( {L_{1}^{2} + L_{2}^{2}} )}{2L_{1}L_{2}}} )}}\mspace{20mu} {{{where}\mspace{14mu} L_{0}^{2}} = {x_{1}^{2} + x_{2}^{2}}}\mspace{20mu} {\theta_{1} = {a\; \tan \; 2( {\frac{{{- k_{s}}x_{1}} + {k_{c}x_{2}}}{k_{c}^{2} + k_{s}^{2}},\frac{{k_{c}x_{1}} + {k_{s}x_{2}}}{k_{c}^{2} + k_{s}^{2}}} )}}\mspace{20mu} {where}\mspace{20mu} {k_{c} = {L_{1} + {L_{2}\cos \; \theta_{2}}}}\mspace{20mu} {k_{s} = {L_{2}\sin \; \theta_{2}}}} & ( {{Equation}\mspace{14mu} 34} )\end{matrix}$

Here, a function atan 2 in Equation 34 is a function that returns adrift angle of (x, y) in the coordinate system when represented by atan2(x, y).

The angles θ1 and θ2 calculated from the output y of the expanded plantmodel 560 by the calculation unit 570 in this manner are the targetcommands related to the positions (angles) of the motors, ideal forservo-controlling the motors 2 a and 2 b. Therefore, the calculationresult obtained by the calculation unit 570 is supplied to the servodriver 4 by a supply unit 580 and is provided to servo control (feedbackcontrol) in the servo driver 4. In the control system of the presentembodiment, the model prediction control performed in the standard PLC 5is performed on the basis of the working coordinate system related tothe robot arm 6. Therefore, it is easy to allow the output of the robotarm 6 to ideally track a predetermined command r based on the workingcoordinate system. Furthermore, through the calculation process of thecalculation unit 570, the result of the model prediction control basedon the working coordinate system can be converted to a target commandwhich can be ideally applied to the servo control of the motors 2 a and2 b based on the rotation coordinate system. In this case, since thecalculation process is based on the geometric relation of the apparatusstructure of the robot arm 6, it is possible to ideally avoid occurrenceof an output error (position error) of the robot arm 6 resulting fromaccumulation of computation errors. This is very useful effect inconsidering the trackability of the robot arm 6.

In the standard PLC 5 having the control structure configured in thismanner, the parameter setting method illustrated in FIG. 4 can beapplied to the setting of the weighting coefficients of the evaluationfunction in the model prediction control. Particularly, in thisconfiguration example, since the prediction model of the modelprediction control unit 53 in the standard PLC 5 is based on the workingcoordinate system which is an orthogonal coordinate system, it ispossible to immediately set the weighting coefficients Qf, Q, and R ofthe evaluation function according to the parameter setting method andideally alleviate the load related to the setting. When model predictioncontrol is performed in the standard PLC 5 through such parametersetting, an integration amount serving as a driving source of servocontrol is adjusted ideally in the servo control for tracking using themodel prediction control, it is possible to realize servo controlsuppressing an overshoot.

Sixth Configuration Example

When the actual plant 6 has a plurality of control axes, the controlstructure for servo control illustrated in the first to thirdconfiguration examples is preferably formed in the standard PLC 5 asillustrated in the fourth and fifth configuration examples. With such aconfiguration, it is not necessary to adapt the servo driver 4 to therespective control axes, and it is easy to construct an entire systemfor servo control of the actual plant 6. The system may naturally beconstructed after the servo driver 4 is adapted to the respectivecontrol axes.

REFERENCE SIGNS LIST

-   1 Network-   2 Motor-   3 Load device-   4 Servo driver-   5 Standard PLC-   6 Plant-   6 a Second integrator-   7 Filter unit-   41 First integrator-   42 State acquisition unit-   43 Model prediction control unit-   50 Command generation unit-   51 Integrator-   52 State acquisition unit-   53 Model prediction control unit-   60 Expanded plant-   560 Expanded plant model-   570 Calculation unit-   580 Supply unit-   600 Further expanded plant

1. A method for setting control parameters for model prediction controlrelated to a predetermined control target, the method being executed bya control device having a first integrator to which an offset between apredetermined target command and an output of the predetermined controltarget corresponding to an actual target device which is an actualtarget of servo control is input, in order to allow an output of theactual target device tracks the predetermined target command, whereinthe control device includes a model prediction control unit which has aprediction model that defines a correlation between a predeterminedexpanded state variable related to an expanded control target includingat least the predetermined control target and a control input to theexpanded control target in a form of a predetermined state equation andwhich performs the model prediction control based on the predictionmodel according to a predetermined evaluation function in a predictionsection having a predetermined time width with respect to thepredetermined target command and outputs a value of the control input atleast at an initial time point of the prediction section, apredetermined state variable which is a portion of the predeterminedexpanded state variable and is related to the predetermined controltarget includes a predetermined integral term represented by a productof the offset and a predetermined integral gain, and the setting methodincludes: a time response determining step of determining a desired timeresponse in an optimum servo control structure which includes a virtualintegrator virtually corresponding to the first integrator and isrelated to a virtual control target virtually corresponding to theexpanded control target and in which, when a virtual target command forthe virtual control target is r1, a virtual control input to the virtualcontrol target is a virtual control input u1, and a virtual output ofthe virtual control target is y1, the virtual control input u1 isrepresented by Equation 1 below including a state feedback gain K_(F)and an integral gain K_(I); a gain calculation step of calculating thestate feedback gain K_(F) and the integral gain K_(I) corresponding tothe desired time response; a weighting coefficient calculation step ofcalculating a second weighting coefficient Q and a third weightingcoefficient R among a first weighting coefficient Qf, the secondweighting coefficient Q, and the third weighting coefficient R in apredetermined Riccati equation represented by Equation 3 below on thebasis of the state feedback gain K_(F) and the integral gain K_(I) whenthe control input to the expanded control target is u, the output of theexpanded control target is y, the offset is e, the predetermined statevariable is x, and a state equation related to the predetermined controltarget is represented by Equation 2 below; and a setting step of settingthe second weighting coefficient Q as a weighting coefficientcorresponding to a state quantity cost which is a stage cost related tothe predetermined state variable and setting the third weightingcoefficient R as a weighting coefficient corresponding to a controlinput cost which is a stage cost related to the control input in thepredetermined evaluation function. $\begin{matrix}\lbrack {{Math}.\mspace{11mu} 1} \rbrack & \; \\{{u\; 1} = {{{- K_{F}}x} + {K_{I}{\int{( {{r\; 1} - {y\; 1}} ){dt}}}}}} & ( {{Equation}\mspace{14mu} 1} ) \\\{ {\begin{matrix}{\overset{.}{x} = {{Ax} + {Bu}}} \\{\overset{.}{z} = {{- {Cx}} + r}}\end{matrix},{\begin{bmatrix}\overset{.}{x} \\\overset{.}{z}\end{bmatrix} = {{{\begin{bmatrix}A & 0 \\{- C} & 0\end{bmatrix}\begin{bmatrix}x \\z\end{bmatrix}} + {\begin{bmatrix}B \\0\end{bmatrix}u} + {\begin{bmatrix}0 \\r\end{bmatrix}{where}\mspace{14mu} e}} = {{r - y} = \overset{.}{z}}}}}  & ( {{Equation}\mspace{14mu} 2} ) \\{{{Q_{f}A_{e}} + {A_{e}^{T}Q_{f}} - {Q_{f}B_{e}R^{- 1}B_{e}^{T}Q_{f}} + Q} = 0} & ( {{Equation}\mspace{14mu} 3} ) \\{{{{where}\mspace{14mu} A_{e}} = \begin{bmatrix}A & 0 \\C & 0\end{bmatrix}},{B_{e} = \begin{bmatrix}B \\0\end{bmatrix}}} & \;\end{matrix}$
 2. The control parameter setting method for modelprediction control according to claim 1, wherein in the weightingcoefficient calculation step, the first weighting coefficient Qf isfurther calculated, in the setting step, the first weighting coefficientQf is further set as the weighting coefficient corresponding to theterminal cost related to the predetermined state variable.
 3. Thecontrol parameter setting method for model prediction control accordingto claim 1, wherein the expanded control target includes thepredetermined control target only, and a portion of the predeterminedexpanded state variable is identical to the predetermined statevariable.
 4. The control parameter setting method for model predictioncontrol according to claim 1, wherein the control input is a jerk inputto the predetermined control target, the expanded control targetincludes additional integrator that performs a predetermined integrationprocess with respect to the jerk input in addition to the predeterminedcontrol target, and the prediction model defines a correlation betweenthe jerk input and the predetermined expanded state variable includingthe predetermined state variable related to the predetermined controltarget and a state variable related to the additional integrator.
 5. Thecontrol parameter setting method for model prediction control accordingto claim 4, wherein a filter unit that performs an attenuation processat a predetermined frequency with respect to a control input based onthe predetermined target command is included in the predeterminedcontrol target and the expanded control target including the additionalintegrator whereby a further expanded control target is formed in thecontrol device, the control parameter setting method for the modelprediction control is executed by the control device, a state variablerelated to the further expanded control target includes a state variablerelated to the filter unit in addition to the predetermined expandedstate variable, the prediction model defines a correlation between thejerk input and the predetermined expanded state variable and the statevariable related to the filter unit, in the weighting coefficientcalculation step, the second weighting coefficient Q and the thirdweighting coefficient R are calculated on the basis of the statefeedback gain K_(F) and the integral gain K_(I), and zeros are added tothe second weighting coefficient as a weighting coefficientcorresponding to the state variable related to the filter unit so as tocorrespond to the further expanded control target to obtain a new secondweighting coefficient, and in the setting step, the new second weightingcoefficient is set as the weighting coefficient corresponding to thestate quantity cost and the third weighting coefficient R is set as theweighting coefficient corresponding to the control input cost in thepredetermined evaluation function.
 6. The control parameter settingmethod for model prediction control according to claim 2, wherein thecontrol input is a jerk input to the predetermined control target, theexpanded control target includes additional integrator that performs apredetermined integration process with respect to the jerk input inaddition to the predetermined control target, and the prediction modeldefines a correlation between the jerk input and the predeterminedexpanded state variable including the predetermined state variablerelated to the predetermined control target and a state variable relatedto the additional integrator.
 7. The control parameter setting methodfor model prediction control according to claim 6, wherein a filter unitthat performs an attenuation process at a predetermined frequency withrespect to a control input based on the predetermined target command isincluded in the predetermined control target and the expanded controltarget including the additional integrator whereby a further expandedcontrol target is formed in the control device, the control parametersetting method for the model prediction control is executed by thecontrol device, a state variable related to the further expanded controltarget includes a state variable related to the filter unit in additionto the predetermined expanded state variable, the prediction modeldefines a correlation between the jerk input and the predeterminedexpanded state variable and the state variable related to the filterunit, in the weighting coefficient calculation step, the first weightingcoefficient Qf, the second weighting coefficient Q, and the thirdweighting coefficient R corresponding to the expanded control target arecalculated on the basis of the state feedback gain K_(F) and theintegral gain K_(I), and zeros are added to the second weightingcoefficient as a weighting coefficient corresponding to a state variablerelated to the filter unit so as to correspond to the further expandedcontrol target to obtain a new second weighting coefficient, and in thesetting step, the first weighting coefficient Qf is set as the weightingcoefficient corresponding to the terminal cost, the new second weightingcoefficient is set as the weighting coefficient corresponding to thestate quantity cost, and the third weighting coefficient R is set as theweighting coefficient corresponding to the control input cost in thepredetermined evaluation function.
 8. The control parameter settingmethod for model prediction control according to claim 5, wherein thefilter unit is configured as a notch filter in which the predeterminedfrequency is used as a central frequency of the attenuation process or alow-pass filter in which the predetermined frequency is used as a cutofffrequency of the attenuation process.